Masonry
(Systematic Rehabilitation)
7.
7.1
Scope
masonry, and hollow clay tile. Stone or glass block
masonry is not covered in this chapter.
This chapter describes engineering procedures for
estimating seismic performance of vertical lateralforce-resisting masonry elements. The methods are
applicable for masonry wall and infill panels that are
either existing or rehabilitated elements of a building
system, or new elements that are added to an existing
building system.
This chapter presents the information needed for
systematic rehabilitation of masonry buildings as
depicted in Step 3 of the Process Flow chart shown in
Figure 1-1. A brief historical perspective is given in
Section 7.2, with an expanded version in Commentary
Section C7.2. Masonry material properties for new and
existing construction are discussed in Section 7.3.
Attributes of masonry walls and masonry infills are
given in Sections 7.4 and 7.5, respectively. Masonry
components are classified by their behavior;
unreinforced components precede reinforced
components, and in-plane action is separated from outof-plane action. For each component type, the
information needed to model stiffness is presented first,
followed by recommended strength and deformation
acceptance criteria for various performance levels.
These attributes are presented in a format for direct use
with the Linear and Nonlinear Static Procedures
prescribed in Chapter 3. Guidelines for anchorage to
masonry walls and masonry foundation elements are
given in Sections 7.6 and 7.7, respectively. Section 7.8
provides definitions for terms used in this chapter, and
Section 7.9 lists the symbols used in Chapter 7
equations. Applicable reference standards are listed in
Section 7.10.
The properties and behavior of steel, concrete, and
timber floor or roof diaphragms are addressed in
Chapters 5, 6, and 8, respectively. Connections to
masonry walls are addressed in Section 7.6 for cases
where behavior of the connection is dependent on
properties of the masonry. Attributes for masonry
foundation elements are briefly described in
Section 7.7.
Unreinforced masonry buildings with flexible floor
diaphragms may be evaluated by using the procedures
given in Appendix C of FEMA 178 (BSSC, 1992) if the
simplified rehabilitation approach of Chapter 10 is
followed.
7.2
Historical Perspective
Construction of existing masonry buildings in the
United States dates back to the 1500s in the
southeastern and southwestern parts of the country, to
the 1770s in the central and eastern parts, and to the
1850s in the western half of the nation. The stock of
existing masonry buildings in the United States largely
comprises structures constructed in the last 150 years.
Since the types of units, mortars, and construction
methods have changed over this course of time,
knowing the vintage of a masonry building may be
useful in identifying the characteristics of the
construction. Although structural properties cannot be
inferred solely from age, some background on typical
materials and methods for a given period can help to
improve engineering judgment, and provide some
direction in the assessment of an existing building.
Portions of a masonry building that are not subject to
systematic rehabilitation provisions of this chapter—
such as parapets, cladding, or partition walls—shall be
considered with the Simplified Rehabilitation options of
Chapter 10 or with the provisions for nonstructural
components addressed in Chapter 11.
As indicated in Chapter 1, great care should be
exercised in selecting the appropriate rehabilitation
approaches and techniques for application to historic
buildings in order to preserve their unique
characteristics.
The provisions of this chapter are intended for solid or
hollow clay-unit masonry, solid or hollow concrete-unit
Section C7.2 of the Commentary provides an extensive
historical perspective on various masonry materials and
construction practices.
FEMA 273
Seismic Rehabilitation Guidelines
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Chapter 7: Masonry
(Systematic Rehabilitation)
7.3
7.3.1
Material Properties and
Condition Assessment
7.3.2
7.3.2.1
Properties of In-Place Materials
Masonry Compressive Strength
Expected masonry compressive strength, fme, shall be
measured using one of the following three methods.
General
The methods specified in Section 7.3.2 for
determination of mechanical properties of existing
masonry construction shall be used as the basis for
stiffness and strength attributes of masonry walls and
infill panels, along with the methods described in
Sections 7.4 and 7.5. Properties of new masonry
components that are added to an existing structural
system shall be based on values given in BSSC (1995).
Minimum requirements for determining in situ masonry
compressive, tensile, and shear strength, as well as
elastic and shear moduli, are provided in Section 7.3.2.
Recommended procedures for measurement of each
material property are described in corresponding
sections of the Commentary. Data from testing of inplace materials shall be expressed in terms of mean
values for determination of expected component
strengths, QCE, and lower bound strengths, QCL, with
the linear or nonlinear procedures described in
Chapter 3.
In lieu of in situ testing, default values of material
strength and modulus, as given in Section 7.3.2, shall be
assigned to masonry components in good, fair, and poor
condition. Default values represent typical lower bound
estimates of strength or stiffness for all masonry
nationwide, and thus should not be construed as
expected values for a specific structure. As specified in
Section 7.3.4, certain in situ tests are needed to attain
the comprehensive level of knowledge (a κ value of
1.00) needed in order to use the nonlinear procedures of
Chapter 3. Thus, unless noted otherwise, general use of
the default values without in situ testing is limited to the
linear procedures of Chapter 3.
Procedures for defining masonry structural systems,
and assessing masonry condition, shall be conducted in
accordance with provisions stated in Section 7.3.3.
Requirements for either a minimum or a comprehensive
level of evaluation, as generally stated in Section 2.7,
are further refined for masonry components in
Section 7.3.4.
1. Test prisms shall be extracted from an existing wall
and tested per Section 1.4.B.3 of the Masonry
Standards Joint Committee’s Building Code
Requirements for Masonry Structures (MSJC,
1995a).
2. Prisms shall be fabricated from actual extracted
masonry units, and a surrogate mortar designed on
the basis of a chemical analysis of actual mortar
samples. The test prisms shall be tested per
Section 1.4.B.3 of the Specification for Masonry
Structures (MSJC, 1995b).
3. Two flat jacks shall be inserted into slots cut into
mortar bed joints and pressurized until peak stress is
reached.
For each of the three methods, the expected
compressive strength shall be based on the net mortared
area.
If the masonry unit strength and the mortar type are
known, fme values may be taken from Tables 1 and 2 of
MSJC (1995a) for clay or concrete masonry constructed
after 1960. The fme value shall be obtained by
multiplying the table values by a factor that represents
both the ratio of expected to lower bound strength and
the height-to-thickness ratio of the prism (see
Commentary Section C7.3.2.1).
In lieu of material tests, default values for masonry
prism compressive strength shall be taken to not exceed
900 psi for masonry in good condition, 600 psi for
masonry in fair condition, and 300 psi for masonry in
poor condition.
7.3.2.2
Masonry Elastic Modulus in
Compression
Expected values of elastic modulus for masonry in
compression, Eme, shall be measured using one of the
following two methods:
1. Test prisms shall be extracted from an existing wall,
transported to a laboratory, and tested in
7-2
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
compression. Stresses and deformations shall be
measured to infer modulus values.
test. Expected shear strength shall be determined in
accordance with Equation 7-1.
2. Two flat jacks shall be inserted into slots cut into
mortar bed joints, and pressurized up to nominally
one half of the expected masonry compressive
strength. Deformations between the two flat jacks
shall be measured to infer compressive strain, and
thus elastic modulus.

P CE
-
0.75  0.75v te + --------An 

v me = --------------------------------------------------1.5
In lieu of prism tests, values for the modulus of
elasticity of masonry in compression shall be taken as
550 times the expected masonry compressive strength,
fme .
7.3.2.3
Masonry Flexural Tensile Strength
Expected flexural tensile strength, fte, for out-of-plane
bending shall be measured using one of the following
three methods:
1. Test samples shall be extracted from an existing
wall, and subjected to minor-axis bending using the
bond-wrench method.
2. Test samples shall be tested in situ using the bondwrench method.
3. Sample wall panels shall be extracted and subjected
to minor-axis bending in accordance with ASTM
E 518.
In lieu of material tests, default values of masonry
flexural tensile strength for walls or infill panels loaded
normal to their plane shall be taken to not exceed 20 psi
for masonry in good condition, 10 psi for masonry in
fair condition, and zero psi for masonry in poor
condition. For masonry constructed after 1960 with
cement-based mortars, default values of flexural tensile
strength can be based on values from Table 8.3.10.5.1
of BSSC (1995).
Flexural tensile strength for unreinforced masonry
(URM) walls subjected to in-plane lateral forces shall
be assumed to be equal to that for out-of-plane bending,
unless testing is done to define expected tensile
strength.
7.3.2.4
Masonry Shear Strength
For URM components, expected masonry shear
strength, vme, shall be measured using the in-place shear
FEMA 273
(7-1)
where
PCE
An
= Expected gravity compressive force applied
to a wall or pier component stress
considering load combinations given in
Equations 3-14, 3-15, and 3-16
= Area of net mortared/grouted section, in.2
vte
= Average bed-joint shear strength, psi
The 0.75 factor on the vte term may be waived for single
wythe masonry, or if the collar joint is known to be
absent or in very poor condition.
Values for the mortar shear strength, vte, shall not
exceed 100 psi for the determination of vme in
Equation 7-1.
Average bed-joint shear strength, vte, shall be
determined from individual shear strength test values,
vto , in accordance with Equation 7-2.
V test
- – pD + L
v to = ---------Ab
(7-2)
where Vtest is the load at first movement of a masonry
unit, Ab is the net mortared area of the bed joints above
and below the test brick, and pD+L is the estimated
gravity stress at the test location.
In lieu of material tests, default values of shear strength
of URM components shall be taken to not exceed 27 psi
for running bond masonry in good condition, 20 psi for
running bond masonry in fair condition, and 13 psi for
running bond masonry in poor condition. These values
shall also be used for masonry in other than running
bond if fully grouted. For masonry in other than running
bond and partially grouted or ungrouted, shear strength
shall be reduced by 60% of these values. For masonry
constructed after 1960 with cement-based mortars,
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Chapter 7: Masonry
(Systematic Rehabilitation)
default values of shear strength can be based on values
in BSSC (1995) for unreinforced masonry.
The in-place shear test shall not be used to estimate
shear strength of reinforced masonry (RM)
components. The expected shear strength of RM
components shall be in accordance with
Section 7.4.4.2A.
7.3.2.5
Masonry Shear Modulus
The expected shear modulus of uncracked,
unreinforced, or reinforced masonry, Gme, shall be
estimated as 0.4 times the elastic modulus in
compression. After cracking, the shear modulus shall be
taken as a fraction of this value based on the amount of
bed joint sliding or the opening of diagonal tension
cracks.
7.3.2.6
Strength and Modulus of Reinforcing
Steel
The expected yield strength of reinforcing bars, fye,
shall be based on mill test data, or tension tests of actual
reinforcing bars taken from the subject building.
Tension tests shall be done in accordance with ASTM
A 615.
In lieu of tension tests of reinforcing bars, default
values of yield stress shall be determined per
Section 6.3.2.5. These values shall also be considered
as lower bound values, fy , to be used to estimate lower
bound strengths, QCL.
The expected modulus of elasticity of steel
reinforcement, Ese, shall be assumed to be 29,000,000
psi.
7.3.2.7
Location and Minimum Number of
Tests
The number and location of material tests shall be
selected to provide sufficient information to adequately
define the existing condition of materials in the
building. Test locations shall be identified in those
masonry components that are determined to be critical
to the primary path of lateral-force resistance.
A visual inspection of masonry condition shall be done
in conjunction with any in situ material tests to assess
uniformity of construction quality. For masonry with
consistent quality, the minimum number of tests for
each masonry type, and for each three floors of
7-4
construction or 3000 square feet of wall surface, shall
be three, if original construction records are available
that specify material properties, or six, if original
construction records are not available. At least two tests
should be done per wall, or line of wall elements
providing a common resistance to lateral forces. A
minimum of eight tests should be done per building.
Tests should be taken at locations representative of the
material conditions throughout the entire building,
taking into account variations in workmanship at
different story levels, variations in weathering of the
exterior surfaces, and variations in the condition of the
interior surfaces due to deterioration caused by leaks
and condensation of water and/or the deleterious effects
of other substances contained within the building.
For masonry with perceived inconsistent quality,
additional tests shall be done as needed to estimate
material strengths in regions where properties are
suspected to differ. Nondestructive condition
assessment tests per Section 7.3.3.2 may be used to
quantify variations in material strengths.
An increased sample size may be adopted to improve
the confidence level. The relation between sample size
and confidence shall be as defined in ASTM E 22.
If the coefficient of variation in test measurements
exceeds 25%, additional tests shall be done. If the
variation does not reduce below this limit, use of the
test data shall be limited to the Linear Static Procedures
of Chapter 3.
If mean values from in situ material tests are less than
the default values prescribed in Section 7.3.2, additional
tests shall be done. If the mean continues to be less than
the default values, the measured values shall be used,
and shall be used only with the Linear Static Procedures
of Chapter 3.
7.3.3
7.3.3.1
Condition Assessment
Visual Examination
The size and location of all masonry shear and bearing
walls shall be determined. The orientation and
placement of the walls shall be noted. Overall
dimensions of masonry components shall be measured,
or determined from plans, including wall heights,
lengths, and thicknesses. Locations and sizes of window
and door openings shall be measured, or determined
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
from plans. The distribution of gravity loads to bearing
walls should be estimated.
• mechanical pulse velocity
• impact echo
The wall type shall be identified as reinforced or
unreinforced, composite or noncomposite, and/or
grouted, partially grouted, or ungrouted. For RM
construction, the size and spacing of horizontal and
vertical reinforcement should be estimated. For
multiwythe construction, the number of wythes should
be noted, as well as the distance between wythes (the
thickness of the collar joint or cavity), and the
placement of interwythe ties. The condition and
attachment of veneer wythes should be noted. For
grouted construction, the quality of grout placement
should be assessed. For partially grouted walls, the
locations of grout placement should be identified.
The type and condition of the mortar and mortar joints
shall be determined. Mortar shall be examined for
weathering, erosion, and hardness, and to identify the
condition of any repointing, including cracks, internal
voids, weak components, and/or deteriorated or eroded
mortar. Horizontal cracks in bed joints, vertical cracks
in head joints and masonry units, and diagonal cracks
near openings shall be noted.
The examination shall identify vertical components that
are not straight. Bulging or undulations in walls shall be
observed, as well as separation of exterior wythes, outof-plumb walls, and leaning parapets or chimneys.
Connections between masonry walls, and between
masonry walls and floors or roofs, shall be examined to
identify details and condition. If construction drawings
are available, a minimum of three connections shall be
inspected for each general connection type (e.g., floorto-wall, wall-to-wall). If no deviations from the
drawings are found, the sample may be considered
representative. If drawings are unavailable, or
significant deviations are noted between the drawings
and constructed work, then a random sample of
connections shall be inspected until a representative
pattern of connections can be identified.
7.3.3.2
Nondestructive Tests
Nondestructive tests may be used to supplement the
visual observations required in Section 7.3.3.1. One, or
a combination, of the following nondestructive tests,
shall be done to meet the requirements of a
comprehensive evaluation as stated in Section 7.3.4:
• radiography
The location and number of nondestructive tests shall
be in accordance with the requirements of
Section 7.3.2.7. Descriptive information concerning
these test procedures is provided in the Commentary,
Section C7.3.3.2.
7.3.3.3
Supplemental Tests
Ancillary tests are recommended, but not required, to
enhance the level of confidence in masonry material
properties, or to assess condition. These are described in
the Commentary to this section.
7.3.4
Knowledge (κ ) Factor
In addition to those characteristics specified in
Section 2.7.2, a knowledge factor, κ, equal to 0.75,
representing a minimum level of knowledge of the
structural system, shall be used if a visual examination
of masonry structural components is done per the
requirements of Section 7.3.3.1. A knowledge factor, κ,
equal to 1.00, shall be used only with a comprehensive
level of knowledge of the structural system (as defined
in Section 2.7.2).
7.4
Engineering Properties of
Masonry Walls
This section provides basic engineering information for
assessing attributes of structural walls, and includes
stiffness assumptions, strength acceptance criteria, and
deformation acceptance criteria for the Immediate
Occupancy, Life Safety, and Collapse Prevention
Performance Levels. Engineering properties given for
masonry walls shall be used with the analytical methods
prescribed in Chapter 3, unless otherwise noted.
Masonry walls shall be categorized as primary or
secondary elements. Walls that are considered to be part
of the lateral-force system, and may or may not support
gravity loads, shall be primary elements. Walls that are
not considered as part of the lateral-force-resisting
system, but must remain stable while supporting gravity
loads during seismic excitation, shall be secondary
elements.
• ultrasonic pulse velocity
FEMA 273
Seismic Rehabilitation Guidelines
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Chapter 7: Masonry
(Systematic Rehabilitation)
7.4.1
Types of Masonry Walls
The procedures set forth in this section are applicable to
building systems comprising any combination of
existing masonry walls, masonry walls enhanced for
seismic rehabilitation, and new walls added to an
existing building for seismic rehabilitation. In addition,
any of these three categories of masonry elements can
be used in combination with existing, rehabilitated, or
new lateral-force-resisting elements of other materials
such as steel, concrete, or timber.
When analyzing a system comprising existing masonry
walls, rehabilitated masonry walls, and/or new masonry
walls, expected values of strength and stiffness shall be
used.
7.4.1.1
Wall types shall include unreinforced or reinforced;
ungrouted, partially grouted, or fully grouted; and
composite or noncomposite. Existing walls subjected to
lateral forces applied parallel with their plane shall be
considered separately from walls subjected to forces
applied normal to their plane, as described in
Sections 7.4.2 through 7.4.5.
Material properties for existing walls shall be
established per Section 7.3.2. Prior to rehabilitation,
masonry structural walls shall be assessed for condition
per the procedures set forth in Sections 7.3.3.1, 7.3.3.2,
or 7.3.3.3. Existing masonry walls shall be assumed to
behave in the same manner as new masonry walls,
provided that the condition assessment demonstrates
equivalent quality of construction.
New Masonry Walls
New masonry walls shall include all new elements
added to an existing lateral-force-resisting system. Wall
types shall include unreinforced or reinforced;
ungrouted, partially grouted, or fully grouted; and
composite or noncomposite. Design of newly
constructed walls shall follow the requirements set forth
in BSSC (1995).
When analyzing a system of new and existing walls,
expected values of strength and stiffness shall be used
for the newly constructed walls. Any capacity reduction
factors given in BSSC (1995) shall not be used, and
7-6
New walls subjected to lateral forces applied parallel
with their plane shall be considered separately from
walls subjected to forces applied normal to their plane,
as described in Sections 7.4.2 through 7.4.5.
7.4.1.3
Enhanced Masonry Walls
Enhanced masonry walls shall include existing walls
that are rehabilitated with the methods given in this
section. Unless stated otherwise, methods are applicable
to both unreinforced and reinforced walls, and are
intended to improve performance of masonry walls
subjected to both in-plane and out-of-plane lateral
forces.
Existing Masonry Walls
Existing masonry walls considered in Section 7.4 shall
include all structural walls of a building system that are
in place prior to seismic rehabilitation.
7.4.1.2
mean values of material strengths shall be used in lieu
of lower bound estimates.
Enhanced walls subjected to lateral forces applied
parallel with their plane shall be considered separately
from walls subjected to forces applied normal to their
plane, as described in Sections 7.4.2 through 7.4.5.
A. Infilled Openings
An infilled opening shall be considered to act
compositely with the surrounding masonry if the
following provisions are met.
1. The sum of the lengths of all openings in the
direction of in-plane shear force in a single
continuous wall is less than 40% of the overall
length of the wall.
2. New and old masonry units shall be interlaced at the
boundary of the infilled opening with full toothing,
or adequate anchorage shall be provided to give an
equivalent shear strength at the interface of new and
old units.
Stiffness assumptions, strength criteria, and acceptable
deformations for masonry walls with infilled openings
shall be the same as given for nonrehabilitated solid
masonry walls, provided that differences in elastic
moduli and strengths for the new and old masonries are
considered for the composite section.
B. Enlarged Openings
Openings in a masonry shear wall may be enlarged by
removing portions of masonry above or below windows
or doors. This is done to increase the height-to-length
aspect ratio of piers so that the limit state may be altered
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
from shear to flexure. This method is only applicable to
URM walls.
Grout in new reinforced cores should consist of
cementitious materials whose hardened properties are
compatible with those of the surrounding masonry.
Stiffness assumptions, strength criteria, and acceptable
deformations for URM walls with enlarged openings
shall be the same as given for existing perforated
masonry walls, provided that the cutting operation does
not cause any distress.
Adequate shear strength must exist, or be provided, so
that the strength of the new vertical reinforcement can
be developed.
C. Shotcrete
Stiffness assumptions, strength criteria, and acceptable
deformations for URM walls with reinforced cores shall
be the same as for existing reinforced walls.
An existing masonry wall with an application of
shotcrete shall be considered to behave as a composite
section, as long as adequate anchorage is provided at
the shotcrete-masonry interface for shear transfer.
Stresses in the masonry and shotcrete shall be
determined considering the difference in elastic moduli
for each material. Alternatively, the masonry may be
neglected if the new shotcrete layer is designed to resist
all of the force, and minor cracking of the masonry is
acceptable.
Stiffness assumptions, strength criteria, and acceptable
deformations for masonry components with shotcrete
shall be the same as for new reinforced concrete
components, with due consideration to possible
variations in boundary conditions.
F.
Prestressed Cores for URM Walls
A prestressed-cored masonry wall with unbonded
tendons shall be considered to behave as a URM wall
with increased vertical compressive stress.
Losses in prestressing force due to creep and shrinkage
of the masonry shall be accounted for.
Stiffness assumptions, strength criteria, and acceptable
deformations for URM walls with unbonded
prestressing tendons shall be the same as for existing
unreinforced masonry walls subjected to vertical
compressive stress.
G. Grout Injections
D. Coatings for URM Walls
A coated masonry wall shall be considered to behave as
a composite section, as long as adequate anchorage is
provided at the interface between the coating and the
masonry wall. Stresses in the masonry and coating shall
be determined considering the difference in elastic
moduli for each material. If stresses exceed expected
strengths of the coating material, then the coating shall
be considered ineffective.
Stiffness assumptions, strength criteria, and acceptable
deformations for coated masonry walls shall be the
same as for existing URM walls.
E. Reinforced Cores for URM Walls
A reinforced-cored masonry wall shall be considered to
behave as a reinforced masonry wall, provided that
sufficient bonding exists between the new reinforcement
and the grout, and between the grout and the cored
surface. Vertical reinforcement shall be anchored at the
base of the wall to resist its full tensile strength.
FEMA 273
Any grout used for filling voids and cracks shall have
strength, modulus, and thermal properties compatible
with the existing masonry.
Inspection shall be made during the grouting to ensure
that voids are completely filled with grout.
Stiffness assumptions, strength criteria, and acceptable
deformations for masonry walls with grout injections
shall be the same as for existing unreinforced or
reinforced walls.
H. Repointing
Bond strength of new mortar shall be equal to or greater
than that of the original mortar. Compressive strength of
new mortar shall be equal to or less than that of the
original mortar.
Stiffness assumptions, strength criteria, and acceptable
deformations for repointed masonry walls shall be the
same as for existing masonry walls.
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Chapter 7: Masonry
(Systematic Rehabilitation)
I.
Braced Masonry Walls
Masonry walls may be braced with external structural
elements to reduce span lengths for out-of-plane
bending. Adequate strength shall be provided in the
bracing element and connections to resist the transfer of
forces from the masonry wall to the bracing element.
Out-of-plane deflections of braced walls resulting from
the transfer of vertical floor or roof loadings shall be
considered.
accordance with the guidelines of this subsection. The
lateral stiffness of masonry walls subjected to lateral inplane forces shall be determined considering both
flexural and shear deformations.
The masonry assemblage of units, mortar, and grout
shall be considered to be a homogeneous medium for
stiffness computations with an expected elastic modulus
in compression, Eme , as specified in Section 7.3.2.2.
Stiffness assumptions, strength criteria, and acceptable
deformations for braced masonry walls shall be the
same as for existing masonry walls. Due consideration
shall be given to the reduced span of the masonry wall.
For linear procedures, the stiffness of a URM wall or
pier resisting lateral forces parallel with its plane shall
be considered to be linear and proportional with the
geometrical properties of the uncracked section.
J.
For nonlinear procedures, the in-plane stiffness of URM
walls or piers shall be based on the extent of cracking.
Stiffening Elements
Masonry walls may be stiffened with external structural
members to increase the out-of-plane stiffness and
strength. The stiffening member shall be proportioned
to resist a tributary portion of lateral load applied
normal to the plane of a masonry wall. Adequate
connections at the ends of the stiffening element shall
be provided to transfer the reaction of force. Flexibility
of the stiffening element shall be considered when
estimating lateral drift of a masonry wall panel for
Performance Levels.
Stiffness assumptions, strength criteria, and acceptable
deformations for stiffened masonry walls shall be the
same as for existing masonry walls. Due consideration
shall be given to the stiffening action that the new
element provides.
7.4.2
URM In-Plane Walls and Piers
Information is given in this section for depicting the
engineering properties of URM walls subjected to
lateral forces applied parallel with their plane.
Requirements of this section shall apply to cantilevered
shear walls that are fixed against rotation at their base,
and piers between window or door openings that are
fixed against rotation at their top and base.
Stiffness and strength criteria are presented that are
applicable for use with both the Linear Static and
Nonlinear Static Procedures prescribed in Chapter 3.
7.4.2.1
Stiffness
The lateral stiffness of masonry wall and pier
components shall be determined based on the minimum
net sections of mortared and grouted masonry in
7-8
Story shears in perforated shear walls shall be
distributed to piers in proportion to the relative lateral
uncracked stiffness of each pier.
Stiffnesses for existing, enhanced, and new walls shall
be determined using the same principles of mechanics.
7.4.2.2
Strength Acceptance Criteria
Unreinforced masonry walls and piers shall be
considered as deformation-controlled components if
their expected lateral strength limited by bed-joint
sliding shear stress or rocking (the lesser of values
given by Equations 7-3 and 7-4) is less than the lower
bound lateral strength limited by diagonal tension or toe
compressive stress (the lesser of values given by
Equations 7-5 or 7-6). Otherwise, these components
shall be considered as force-controlled components.
A. Expected Lateral Strength of Walls and Piers
Expected lateral strength of existing URM walls or pier
components shall be based on expected bed-joint
sliding shear strength, or expected rocking strength, in
accordance with Equations 7-3 and 7-4, respectively.
The strength of such URM walls or piers shall be the
lesser of:
(7-3)
Q CE = V bjs = v me A n
L
Q CE = V r = 0.9 α P CE  --------
h
Seismic Rehabilitation Guidelines
(7-4)
eff
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
where An , heff , L, and α are the same as given for
Equations 7-3 and 7-4, and:
where
An
= Area of net mortared/grouted section, in.2
heff
= Height to resultant of lateral force
fa
L
= Length of wall or pier
PCE = Expected vertical axial compressive force per
load combinations in Equations 3-2 and 3-3
vme = Expected bed-joint sliding shear strength per
Section 7.3.2.4, psi
Vbjs = Lateral strength of wall or pier based on bedjoint shear strength, pounds
Vr
= Lateral rocking strength of wall or pier
component, pounds
= Factor equal to 0.5 for fixed-free cantilever
α
wall, or equal to 1.0 for fixed-fixed pier
Expected lateral strength of newly constructed wall or
pier components shall be based on the NEHRP
Recommended Provisions (BSSC, 1995), with the
exception that capacity reduction factors shall be taken
as equal to 1.0.
B. Lower Bound Lateral Strength of Walls and Piers
Lower bound lateral strength of existing URM walls or
pier components shall be limited by diagonal tension
stress or toe compressive stress, in accordance with
Equations 7-5 and 7-6, respectively. The lateral strength
of URM walls or piers shall be the lesser of Q CL values
given by these two equations.
If L /heff is larger than 0.67 and less than 1.00, then:
L
′ A n  -------- 1 +
Q CL = V dt = f dt
h 
eff
fa
------′
f dt
fa 
L 
-
Q CL = V tc = α P CL  --------  1 – -------------h eff 
0.7f ′m 
(7-5)
(7-6)
′
f dt
′
fm
PCL
Vdt
Vtc
= Upper bound of vertical axial compressive
stress from Equation 3-2, psi
= Lower bound of masonry diagonal tension
strength, psi
= Lower bound of masonry compressive
strength, psi
= Lower bound of vertical compressive force
from load combination of Equation 3-3,
pounds
= Lateral strength limited by diagonal tension
stress, pounds
= Lateral strength limited by toe compressive
stress, pounds
For determination of Vdt, the bed-joint shear strength,
vme, may be substituted for the diagonal tension
′ , in Equation 7-5.
strength, f dt
The lower bound masonry compressive strength, f m
′ ,
shall be taken as the expected strength, fme , determined
per Section 7.3.2.1, divided by 1.6.
If the Linear Static Procedures of Section 3.3 are used,
lateral forces from gravity and seismic effects shall be
less than the lower bound lateral strength, QCL, as
required by Equation 3-19.
C. Lower Bound Vertical Compressive Strength of
Walls and Piers
Lower bound vertical compressive strength of existing
URM walls or pier components shall be limited by
masonry compressive stress per Equation 7-7.
′ An )
Q CL = P c = 0.80 ( 0.85f m
(7-7)
where f ′m is equal to the expected strength, fme,
determined per Section 7.3.2.1, divided by 1.6.
If the Linear Static Procedures of Section 3.3 are used,
vertical forces from gravity and seismic effects shall be
less than the lower bound lateral strength, QCL, as stated
in Equation 3-19.
FEMA 273
Seismic Rehabilitation Guidelines
7-9
Chapter 7: Masonry
(Systematic Rehabilitation)
7.4.2.3
Deformation Acceptance Criteria
A. Linear Procedures
Table 7-1
Linear Static Procedure—m Factors for URM In-Plane Walls and Piers
m Factors
Limiting
Behavioral Mode
Bed-Joint Sliding
Rocking
Primary
Secondary
IO
LS
CP
LS
CP
1
3
4
6
8
(1.5heff/L)>1
(3heff/L)>1.5
(4heff/L)>2
(6heff/L)>3
(8heff/L)>4
Note: Interpolation is permitted between table values.
If the linear procedures of Section 3.3 are used, the
product of expected strength, QCE, of those components
classified as deformation-controlled, multiplied by m
factors given in Table 7-1 for particular Performance
Levels and κ factors given in Section 2.7.2, shall exceed
the sum of unreduced seismic forces, QE, and gravity
forces, QG, per Equation 3-18. The limiting behavior
mode in Table 7-1 shall be identified from the lower of
the two expected strengths as determined from
Equations 7-3 and 7-4.
For determination of m factors from Table 7-1, the
vertical compressive stress, fae , shall be based on an
expected value of gravity compressive force given by
the load combinations given in Equations 3-2 and 3-3.
B. Nonlinear Procedures
If the Nonlinear Static Procedure given in Section 3.3.3
is used, deformation-controlled wall and pier
components shall be assumed to deflect to nonlinear
lateral drifts as given in Table 7-2. Variables d and e,
representing nonlinear deformation capacities for
primary and secondary components, are expressed in
terms of story drift ratio percentages, as defined in
Figure 7-1.The limiting behavior mode in Table 7-2
shall be identified from the lower of the two expected
strengths as determined from Equations 7-3 and 7-4.
For components of primary lateral-force-resisting
elements, collapse shall be considered at lateral drift
percentages exceeding values of d in the table, and the
Life Safety Performance Level shall be considered at
approximately 75% of the d value. For components of
7-10
e
Q
Qexp
d
1.0
c
∆eff
heff
Figure 7-1
Idealized Force-Deflection Relation for
Walls, Pier Components, and Infill
Panels
secondary elements, collapse shall be considered at
lateral drift percentages exceeding the values of e in the
table, and the Life Safety Performance Level shall be
considered at approximately 75% of the e value in the
table. Drift percentages based on these criteria are given
in Table 7-2.
If the Nonlinear Dynamic Procedure given in
Section 3.3.4 is used, nonlinear force-deflection
relations for wall and pier components shall be
established based on the information given in Table 7-2,
or on a more comprehensive evaluation of the hysteretic
characteristics of those components.
7.4.3
URM Out-of-Plane Walls
As required by Section 2.11.7, URM walls shall be
considered to resist out-of-plane excitation as isolated
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
Table 7-2
Nonlinear Static Procedure—Simplified Force-Deflection Relations for URM In-Plane Walls
and Piers
Acceptance Criteria
Limiting Behavioral
Mode
Primary
Secondary
c
%
d
%
e
%
IO
%
LS
%
CP
%
LS
%
CP
%
Bed-Joint Sliding
0.6
0.4
0.8
0.1
0.3
0.4
0.6
0.8
Rocking
0.6
0.4heff /L
0.8heff /L
0.1
0.3heff /L
0.4heff /L
0.6heff /L
0.8heff /L
Note: Interpolation is permitted between table values.
components spanning between floor levels, and/or
spanning horizontally between columns or pilasters.
Out-of-plane walls shall not be analyzed with the Linear
or Nonlinear Static Procedures prescribed in Chapter 3.
7.4.3.1
Stiffness
The stiffness of out-of-plane walls shall be neglected
with analytical models of the global structural system if
in-plane walls or infill panels exist, or are placed, in the
orthogonal direction.
7.4.3.2
Strength Acceptance Criteria
The Immediate Occupancy Performance Level shall be
limited by flexural cracking of out-of-plane walls.
Unless arching action is considered, flexural cracking
shall be limited by the expected tensile stress values
given in Section 7.3.2.3 for existing walls and in BSSC
(1995) for new construction.
Arching action shall be considered if, and only if,
surrounding floor, roof, column, or pilaster elements
have sufficient stiffness and strength to resist thrusts
from arching of a wall panel, and a condition
assessment has been done to ensure that there are no
gaps between a wall panel and the adjacent structure.
Due consideration shall be given to the condition of the
collar joint when estimating the effective thickness of a
wall.
7.4.3.3
Deformation Acceptance Criteria
The Life Safety and Collapse Prevention Levels permit
flexural cracking in URM walls subjected to out-ofplane loading, provided that cracked wall segments will
remain stable during dynamic excitation. Stability shall
FEMA 273
be checked using analytical time-step integration
models with realistic depiction of acceleration time
histories at the top and base of a wall panel. Walls
spanning vertically, with a height-to-thickness (h/t)
ratio less than that given in Table 7-3, need not be
checked for dynamic stability.
Table 7-3
Permissible h/t Ratios for URM Outof-Plane Walls
SX1
≤0.24g
0.24g<SX1
≤0.37g
0.37g<SX1
≤0.5g
Walls of one-story
buildings
20
16
13
First-story wall of
multistory building
20
18
15
Walls in top story of
multistory building
14
14
9
All other walls
20
16
13
Wall Types
7.4.4
7.4.4.1
Reinforced Masonry In-Plane Walls
and Piers
Stiffness
The stiffness of a reinforced in-plane wall or pier
component shall be based on:
• The uncracked section, when an analysis is done to
show that the component will not crack when
subjected to expected levels of axial and lateral force
• The cracked section, when an analysis is done to
show that the component will crack when subjected
to expected levels of axial and lateral force
Seismic Rehabilitation Guidelines
7-11
Chapter 7: Masonry
(Systematic Rehabilitation)
Stiffnesses for existing and new walls shall be assumed
to be the same.
7.4.4.2
Strength Acceptance Criteria for
Reinforced Masonry (RM)
Strength of RM wall or pier components in flexure,
shear, and axial compression shall be determined per
the requirements of this section. The assumptions,
procedures, and requirements of this section shall apply
to both existing and newly constructed RM wall or pier
components.
Reinforced masonry walls and piers shall be considered
as deformation-controlled components if their expected
lateral strength for flexure per Section 7.4.4.2A is less
than the lower bound lateral strength limited by shear
per Section 7.4.4.2B. Vertical compressive behavior of
reinforced masonry wall or pier components shall be
assumed to be a force-controlled action. Methods for
determining lower bound axial compressive strength are
given in Section 7.4.4.2D.
A. Expected Flexural Strength of Walls and Piers
Expected flexural strength of an RM wall or pier shall
be determined on the basis of the following
assumptions.
• Stress in reinforcement below the expected yield
strength, fye, shall be taken as the modulus of
elasticity, Ese, times the steel strain. For
reinforcement strains larger than those
corresponding to the expected yield strength, the
stress in the reinforcement shall be considered
independent of strain and equal to the expected yield
strength, fye.
• Tensile strength of masonry shall be neglected in
calculating the flexural strength of a reinforced
masonry cross section.
• Flexural compression stress in masonry shall be
assumed to be distributed across an equivalent
rectangular stress block. Masonry stress of 0.85
times the expected compressive strength, fme, shall
be distributed uniformly over an equivalent
compression zone bounded by edges of the cross
section and with a depth equal to 85% of the depth
from the neutral axis to the fiber of maximum
compressive strain.
7-12
• Strains in the reinforcement and masonry shall be
considered linear across the wall or pier cross
section. For purposes of determining forces in
reinforcing bars distributed across the section, the
maximum compressive strain in the masonry shall
be assumed to be equal to 0.003.
B.
Lower-Bound Shear Strength of Walls and Piers
Lower-bound shear strength of RM wall or pier
components, VCL, shall be determined using
Equation 7-8.
(7-8)
Q CL = V CL = V mL + V sL
where:
= Lower bound shear strength provided by
masonry, lb
= Lower bound shear strength provided by
reinforcement, lb
VmL
VsL
The lower bound shear strength of an RM wall or pier
shall not exceed shear forces given by Equations 7-9
and 7-10.
For M/Vdv less than 0.25:
′ An
V CL ≤ 6 f m
(7-9)
For M/Vdv greater than or equal to 1.00:
V CL ≤ 4 f m′ A n
(7-10)
where:
An
= Area of net mortared/grouted section, in.2
f m′
= Compressive strength of masonry, psi
M
V
dv
= Moment on the masonry section, in.-lb
= Shear on the masonry section, lb
= Wall length in direction of shear force, in.
Lower-bound shear strength, VmL, resisted by the
masonry shall be determined using Equation 7-11.
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
M
V mL = 4.0 – 1.75  --------- A n f m + 0.25P CL (7-11)
Vd v
where M/Vdv need not be taken greater than 1.0, and
PCL is the lower-bound vertical compressive force in
pounds based on the load combinations given in
Equations 3-2 and 3-3.
Lower-bound shear strength, VsL, resisted by the
reinforcement shall be determined using Equation 7-12.
Av
V sL = 0.5  ------ f y d v
s
D. Lower Bound Vertical Compressive Strength of
Walls and Piers
Lower bound vertical compressive strength of existing
RM walls or pier components shall be determined using
Equation 7-13.
′ ( A n – As ) + A s f y ]
Q CL = P c = 0.8 [ 0.85f m
where:
f m′
(7-12)
fy
where:
Av
=
Area of shear reinforcement, in.2
s
fy
=
=
Spacing of shear reinforcement, in.
Lower-bound yield strength of shear
reinforcement, psi
(7-13)
= Lower bound masonry compressive strength
equal to expected strength, fme, determined
per Section 7.3.2.1, divided by 1.6
= Lower bound reinforcement yield strength
per Section 7.3.2.6
If the Linear Static Procedures of Section 3.3.1 are
used, vertical forces from gravity and seismic effects
shall be less than the lower bound lateral strength, QCL,
as required by Equation 3-19.
7.4.4.3
Deformation Acceptance Criteria
C. Strength Considerations for Flanged Walls
A. Linear Procedures
Wall intersections shall be considered effective in
transferring shear when either condition (1) or (2), and
condition (3), as noted below, are met:
If the linear procedures of Section 3.3 are used, the
product of expected strength, QCE, of those components
classified as deformation-controlled, multiplied by m
factors given in Table 7-4 for particular Performance
Levels and κ factors given in Section 2.7.2, shall exceed
the sum, QUD ,of unreduced seismic forces, QE, and
gravity forces, QG, as in Equations 3-14 and 3-18.
1. The face shells of hollow masonry units are removed
and the intersection is fully grouted.
2. Solid units are laid in running bond, and 50% of the
masonry units at the intersection are interlocked.
3. Reinforcement from one intersecting wall continues
past the intersection a distance not less than 40 bar
diameters or 24 inches.
The width of flange considered effective in
compression on each side of the web shall be taken as
equal to six times the thickness of the web, or shall be
equal to the actual flange on either side of the web wall,
whichever is less.
The width of flange considered effective in tension on
each side of the web shall be taken as equal to 3/4 of the
wall height, or shall be equal to the actual flange on
either side of the web wall, whichever is less.
For determination of m factors from Table 7-4, the ratio
of vertical compressive stress to expected compressive
strength, fae /fme, shall be based on an expected value of
gravity compressive force per the load combinations
given in Equations 3-2 and 3-3.
B. Nonlinear Procedures
If the Nonlinear Static Procedure given in Section 3.3.3
is used, deformation-controlled wall and pier
components shall be assumed to deflect to nonlinear
lateral drifts as given in Table 7-5. Variables d and e,
representing nonlinear deformation capacities for
primary and secondary components, are expressed in
terms of story drift ratio percentages as defined in
Figure 7-1.
For determination of the c, d, and e values and the
acceptable drift levels using Table 7-5, the vertical
FEMA 273
Seismic Rehabilitation Guidelines
7-13
Chapter 7: Masonry
(Systematic Rehabilitation)
compressive stress, fae, shall be based on an expected
value of gravity compressive force per the load
combinations given in Equations 3-2 and 3-3.
Section 7.3.2.3. Stiffness shall be based on a cracked
section for a wall whose net flexural tensile stress
exceeds expected tensile strength.
For components of primary lateral-force-resisting
elements, collapse shall be considered at lateral drift
percentages exceeding values of d in Table 7-5, and the
Life Safety Performance Level shall be considered at
approximately 75% of the d value. For components of
secondary elements, collapse shall be considered at
lateral drift percentages exceeding the values of e in the
table, and the Life Safety Performance Level shall be
considered at approximately 75% of the e value in the
table. Story drift ratio percentages based on these
criteria are given in Table 7-5.
Stiffnesses for existing and new reinforced out-of-plane
walls shall be assumed to be the same.
If the Nonlinear Dynamic Procedure given in
Section 3.3.4 is used, nonlinear force-deflection
relations for wall and pier components shall be
established based on the information given in Table 7-5,
or on a more comprehensive evaluation of the hysteretic
characteristics of those components.
Strength of new walls and existing walls shall be
assumed to be the same.
Acceptable deformations for existing and new walls
shall be assumed to be the same.
7.4.5
RM Out-of-Plane Walls
As required by Section 2.11.7, RM walls shall be
considered to resist out-of-plane excitation as isolated
components spanning between floor levels, and/or
spanning horizontally between columns or pilasters.
Out-of-plane walls shall not be analyzed with the Linear
or Nonlinear Static Procedures prescribed in Chapter 3,
but shall resist lateral inertial forces as given in
Section 2.11.7, or respond to earthquake motions as
determined with the Nonlinear Dynamic Procedure and
satisfy the deflection criteria given in Section 7.4.5.3.
7.4.5.1
Stiffness
Out-of-plane RM walls shall be considered as local
elements spanning between individual story levels.
The stiffness of out-of-plane walls shall be neglected
with analytical models of the global structural system if
in-plane walls exist or are placed in the orthogonal
direction.
Uncracked sections based on the net mortared/grouted
area shall be considered for determination of
geometrical properties, provided that net flexural tensile
stress does not exceed expected tensile strength, fte, per
7-14
7.4.5.2
Strength Acceptance Criteria
Out-of-plane RM walls shall be sufficiently strong in
flexure to resist the transverse loadings prescribed in
Section 2.11.7 for all Performance Levels. Expected
flexural strength shall be based on the assumptions
given in Section 7.4.4.2A. For walls with an h/t ratio
exceeding 20, the effects of deflections on moments
shall be considered.
7.4.5.3
Deformation Acceptance Criteria
If the Nonlinear Dynamic Procedure is used, the
following performance criteria shall be based on the
maximum deflection normal to the plane of a transverse
wall.
• The Immediate Occupancy Performance Level shall
be met when significant visual cracking of an RM
wall occurs. This limit state shall be assumed to
occur at a lateral story drift ratio of approximately
2%.
• The Life Safety Performance Level shall be met
when masonry units are dislodged and fall out of the
wall. This limit state shall be assumed to occur at a
lateral drift of a story panel equal to approximately
3%.
• The Collapse Prevention Performance Level shall be
met when the post-earthquake damage state is on the
verge of collapse. This limit state shall be assumed
to occur at a lateral story drift ratio of approximately
5%.
Acceptable deformations for existing and new walls
shall be assumed to be the same.
7.5
Engineering Properties of
Masonry Infills
This section provides basic engineering information for
assessing attributes of masonry infill panels, including
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
Table 7-4
Linear Static Procedure—m Factors for Reinforced Masonry In-Plane Walls
m Factors
Primary
fae /fme
0.00
L /heff
ρgfye /fme
IO
LS
CP
LS
CP
0.5
0.01
4.0
7.0
8.0
8.0
10.0
0.05
2.5
5.0
6.5
8.0
10.0
0.20
1.5
2.0
2.5
4.0
5.0
0.01
4.0
7.0
8.0
8.0
10.0
0.05
3.5
6.5
7.5
8.0
10.0
0.20
1.5
3.0
4.0
6.0
8.0
0.01
4.0
7.0
8.0
8.0
10.0
0.05
3.5
6.5
7.5
8.0
10.0
0.20
2.0
3.5
4.5
7.0
9.0
0.01
3.0
6.0
7.5
8.0
10.0
0.05
2.0
3.5
4.5
7.0
9.0
0.20
1.5
2.0
2.5
4.0
5.0
0.01
4.0
7.0
8.0
8.0
10.0
0.05
2.5
5.0
6.5
8.0
10.0
0.20
1.5
2.5
3.5
5.0
7.0
0.01
4.0
7.0
8.0
8.0
10.0
0.05
3.5
6.5
7.5
8.0
10.0
0.20
1.5
3.0
4.0
6.0
8.0
1.0
2.0
0.038
0.5
1.0
2.0
0.075
Secondary
0.5
1.0
2.0
0.01
2.0
3.5
4.5
7.0
9.0
0.05
1.5
3.0
4.0
6.0
8.0
0.20
1.0
2.0
2.5
4.0
5.0
0.01
2.5
5.0
6.5
8.0
10.0
0.05
2.0
3.5
4.5
7.0
9.0
0.20
1.5
2.5
3.5
5.0
7.0
0.01
4.0
7.0
8.0
8.0
10.0
0.05
2.5
5.0
6.5
8.0
10.0
0.20
1.5
3.0
4.0
4.0
8.0
Note: Interpolation is permitted between table values.
stiffness assumptions, and the strength acceptance and
deformation acceptance criteria for the Immediate
Occupancy, Life Safety, and Collapse Prevention
Performance Levels. Engineering properties given for
masonry infills shall be used with the analytical
methods prescribed in Chapter 3, unless noted
otherwise.
FEMA 273
Masonry infill panels shall be considered as primary
elements of a lateral-force-resisting system. If the
surrounding frame can remain stable following the loss
of an infill panel, infill panels shall not be subject to
limits set by the Collapse Prevention Performance
Level.
Seismic Rehabilitation Guidelines
7-15
Chapter 7: Masonry
(Systematic Rehabilitation)
Table 7-5
Nonlinear Static Procedure—Simplified Force-Deflection Relations for Reinforced Masonry
Shear Walls
Acceptance Criteria
Primary
Secondary
fae/fme
L/heff
ρgfye/fme
c
d
%
e
%
IO
%
LS
%
CP
%
LS
%
CP
%
0.00
0.5
0.01
0.5
2.6
5.3
1.0
2.0
2.6
3.9
5.3
0.05
0.6
1.1
2.2
0.4
0.8
1.1
1.6
2.2
0.20
0.7
0.5
1.0
0.2
0.4
0.5
0.7
1.0
0.01
0.5
2.1
4.1
0.8
1.6
2.1
3.1
4.1
0.05
0.6
0.8
1.6
0.3
0.6
0.8
1.2
1.6
0.20
0.7
0.3
0.6
0.1
0.2
0.3
0.5
0.6
0.01
0.5
1.6
3.3
0.6
1.2
1.6
2.5
3.3
0.05
0.6
0.6
1.3
0.2
0.5
0.6
0.9
1.3
0.20
0.7
0.2
0.4
0.1
0.2
0.2
0.3
0.4
0.01
0.4
1.0
2.0
0.4
0.8
1.0
1.5
2.0
0.05
0.5
0.7
1.4
0.3
0.5
0.7
1.0
1.4
1.0
2.0
0.038
0.5
1.0
2.0
0.075
0.5
1.0
2.0
0.20
0.6
0.4
0.9
0.2
0.3
0.4
0.7
0.9
0.01
0.4
0.8
1.5
0.3
0.6
0.8
1.1
1.5
0.05
0.5
0.5
1.0
0.2
0.4
0.5
0.7
1.0
0.20
0.6
0.3
0.6
0.1
0.2
0.3
0.4
0.6
0.01
0.4
0.6
1.2
0.2
0.4
0.6
0.9
1.2
0.05
0.5
0.4
0.7
0.1
0.3
0.4
0.5
0.7
0.20
0.6
0.2
0.4
0.1
0.1
0.2
0.3
0.4
0.01
0.3
0.6
1.2
0.2
0.5
0.6
0.9
1.2
0.05
0.4
0.5
1.0
0.2
0.4
0.5
0.8
1.0
0.20
0.5
0.4
0.8
0.1
0.3
0.4
0.6
0.8
0.01
0.3
0.4
0.9
0.2
0.3
0.4
0.7
0.9
0.05
0.4
0.4
0.7
0.1
0.3
0.4
0.5
0.7
0.20
0.5
0.2
0.5
0.1
0.2
0.2
0.4
0.5
0.01
0.3
0.3
0.7
0.1
0.2
0.3
0.5
0.7
0.05
0.4
0.3
0.5
0.1
0.2
0.3
0.4
0.5
0.20
0.5
0.2
0.3
0.1
0.1
0.2
0.2
0.3
Note: Interpolation is permitted between table values.
7-16
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
7.5.1
Types of Masonry Infills
Procedures set forth in this section are applicable to
existing panels, panels enhanced for seismic
rehabilitation, and new panels added to an existing
frame. Infills shall include panels built partially or fully
within the plane of steel or concrete frames, and
bounded by beams and columns around their
perimeters.
Infill panel types considered in these Guidelines include
unreinforced clay-unit masonry, concrete masonry, and
hollow-clay tile masonry. Infills made of stone or glass
block are not addressed.
Infill panels that are considered to be isolated from the
surrounding frame must have sufficient gaps at top and
sides to accommodate maximum lateral frame
deflections. Isolated panels shall be restrained in the
transverse direction to insure stability under normal
forces. Panels that are in tight contact with the frame
elements on all four sides are termed shear infill panels.
For panels to be considered under this designation, any
gaps between an infill and a surrounding frame shall be
filled to provide tight contact.
Frame members and connections surrounding infill
panels shall be evaluated for frame-infill interaction
effects. These effects shall include forces transferred
from an infill panel to beams, columns, and
connections, and bracing of frame members across a
partial length.
7.5.1.1
Existing Masonry Infills
Existing masonry infills considered in this section shall
include all structural infills of a building system that are
in place prior to seismic rehabilitation.
Infill types included in this section consist of
unreinforced and ungrouted panels, and composite or
noncomposite panels. Existing infill panels subjected to
lateral forces applied parallel with their plane shall be
considered separately from infills subjected to forces
applied normal to their plane, as described in
Sections 7.5.2 and 7.5.3.
Material properties for existing infills shall be
established per Section 7.3.2. Prior to rehabilitation,
masonry infills shall be assessed for condition per
procedures set forth in Sections 7.3.3.1, 7.3.3.2, or
7.3.3.3. Existing masonry infills shall be assumed to
behave the same as new masonry infills, provided that a
FEMA 273
condition assessment demonstrates equivalent quality
of construction.
7.5.1.2
New Masonry Infills
New masonry infills shall include all new panels added
to an existing lateral-force-resisting system for
structural rehabilitation. Infill types shall include
unreinforced, ungrouted, reinforced, grouted and
partially grouted, and composite or noncomposite.
When analyzing a system of new infills, expected
values of strength and stiffness shall be used. No
capacity reduction factors shall be used, and expected
values of material strengths shall be used in lieu of
lower bound estimates.
7.5.1.3
Enhanced Masonry Infills
Enhanced masonry infill panels shall include existing
infills that are rehabilitated with the methods given in
this section. Unless stated otherwise, methods are
applicable to unreinforced infills, and are intended to
improve performance of masonry infills subjected to
both in-plane and out-of-plane lateral forces.
Masonry infills that are enhanced in accordance with
the minimum standards of this section shall be
considered using the same Analysis Procedures and
performance criteria as for new infills.
Guidelines from the following sections, pertaining to
enhancement methods for unreinforced masonry walls,
shall also apply to unreinforced masonry infill panels:
(1) “Infilled Openings,” Section 7.4.1.3A; (2)
“Shotcrete,” Section 7.4.1.3C; (3) “Coatings for URM
Walls,” Section 7.4.1.3D; (4) “Grout Injections,”
Section 7.4.1.3G; (5) “Repointing,” Section 7.4.1.3H;
and (6) “Stiffening Elements,” Section 7.4.1.3J. In
addition, the following two enhancement methods shall
also apply to masonry infill panels.
A. Boundary Restraints for Infill Panels
Infill panels not in tight contact with perimeter frame
members shall be restrained for out-of-plane forces.
This may be accomplished by installing steel angles or
plates on each side of the infills, and welding or bolting
the angles or plates to the perimeter frame members.
B. Joints Around Infill Panels
Gaps between an infill panel and the surrounding frame
shall be filled if integral infill-frame action is assumed
for in-plane response.
Seismic Rehabilitation Guidelines
7-17
Chapter 7: Masonry
(Systematic Rehabilitation)
7.5.2
In-Plane Masonry Infills
7.5.2.1
analyses that consider the nonlinear behavior of the
infilled frame system after the masonry is cracked.
Stiffness
The elastic in-plane stiffness of a solid unreinforced
masonry infill panel prior to cracking shall be
represented with an equivalent diagonal compression
strut of width, a, given by Equation 7-14. The
equivalent strut shall have the same thickness and
modulus of elasticity as the infill panel it represents.
a = 0.175 ( λ 1 h col )
– 0.4
(7-14)
r inf
The equivalent compression strut analogy shall be used
to represent the elastic stiffness of a perforated
unreinforced masonry infill panel, provided that the
equivalent strut properties are determined from
appropriate stress analyses of infill walls with
representative opening patterns.
Stiffnesses for existing and new infills shall be assumed
to be the same.
7.5.2.2
where
Strength Acceptance Criteria
A. Infill Shear Strength
E me t inf sin 2 θ
λ 1 = -------------------------------4E fe I col h inf
1--4
The transfer of story shear across a masonry infill panel
confined within a concrete or steel frame shall be
considered as a deformation-controlled action.
Expected in-plane panel shear strength shall be
determined per the requirements of this section.
and
hcol
hinf
= Column height between centerlines of
beams, in.
= Height of infill panel, in.
Icol
= Expected modulus of elasticity of frame
material, psi
= Expected modulus of elasticity of infill
material, psi
= Moment of inertia of column, in.4
Linf
= Length of infill panel, in.
rinf
= Diagonal length of infill panel, in.
tinf
= Thickness of infill panel and equivalent strut,
in.
= Angle whose tangent is the infill height-tolength aspect ratio, radians
= Coefficient used to determine equivalent
width of infill strut
Efe
Eme
θ
λ1
Q CE = V ine = A ni f vie
Stiffness of cracked unreinforced masonry infill panels
shall be represented with equivalent struts, provided
that the strut properties are determined from detailed
(7-15)
where:
Ani
For noncomposite infill panels, only the wythes in full
contact with the frame elements shall be considered
when computing in-plane stiffness, unless positive
anchorage capable of transmitting in-plane forces from
frame members to all masonry wythes is provided on all
sides of the walls.
7-18
Expected infill shear strength, Vine, shall be calculated
as the product of the net mortared and grouted area of
the infill panel, Ani, times the expected shear strength of
the masonry, fvie, in accordance with Equation 7-15.
fvie
= Area of net mortared/grouted section across
infill panel, in.2
= Expected shear strength of masonry infill, psi
Expected shear strength of existing infills, fvie, shall be
taken to not exceed the expected masonry bed-joint
shear strength, vme, as determined per Section 7.3.2.4.
Shear strength of newly constructed infill panels, fvie,
shall not exceed values given in Section 8.7.4 of BSSC
(1995) for zero vertical compressive stress.
For noncomposite infill panels, only the wythes in full
contact with the frame elements shall be considered
when computing in-plane strength, unless positive
anchorage capable of transmitting in-plane forces from
frame members to all masonry wythes is provided on all
sides of the walls.
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
B. Required Strength of Column Members Adjacent
to Infill Panels
where:
h inf
tan θ b = ---------------------------a
L inf – ------------sin θ b
Unless a more rigorous analysis is done, the expected
flexural and shear strengths of column members
adjacent to an infill panel shall exceed forces resulting
from one of the following conditions:
1. The application of the horizontal component of the
expected infill strut force applied at a distance, lceff,
from the top or bottom of the infill panel equal to:
a
l ceff = -------------cos θ c
(7-16)
where:
The requirements of this section shall be waived if the
expected masonry shear strength, vme, as measured per
test procedures of Section 7.3.2.4, is less than 50 psi.
(7-17)
The reduced column length, lceff , in Equation 7-16 shall
be equal to the clear height of opening for a captive
column braced laterally with a partial height infill.
The requirements of this section shall be waived if the
expected masonry shear strength, vme, as measured per
test procedures of Section 7.3.2.4, is less than 50 psi.
C. Required Strength of Beam Members Adjacent to
Infill Panels
The expected flexural and shear strengths of beam
members adjacent to an infill panel shall exceed forces
resulting from one of the following conditions:
1. The application of the vertical component of the
expected infill strut force applied at a distance, lbeff ,
from the top or bottom of the infill panel equal to:
a
l ceff = ------------sin θ b
Deformation Acceptance Criteria
A. Linear Procedures
2. The shear force resulting from development of
expected column flexural strengths at the top and
bottom of a column with a reduced height equal to
lceff
FEMA 273
2. The shear force resulting from development of
expected beam flexural strengths at the ends of a
beam member with a reduced length equal to lbeff
7.5.2.3
a
h inf – -------------cos θ
tan θ c = ----------------------------cL inf
(7-19)
(7-18)
If the linear procedures of Section 3.3.1 are used, the
product of expected infill strength, Vine, multiplied by m
factors given in Table 7-6 for particular Performance
Levels and κ factors given in Section 2.7.2, shall exceed
the sum of unreduced seismic forces, QE, and gravity
forces, Q G, per Equation 3-18. For the case of an infill
panel, QE shall be the horizontal component of the
unreduced axial force in the equivalent strut member.
For determination of m factors per Table 7-6, the ratio
of frame to infill strengths shall be determined
considering the expected lateral strength of each
component. If the expected frame strength is less than
0.3 times the expected infill strength, the confining
effects of the frame shall be neglected and the masonry
component shall be evaluated as an individual wall
component per Sections 7.4.2 or 7.4.4.
B. Nonlinear Procedures
If the Nonlinear Static Procedure given in Section 3.3.3
is used, infill panels shall be assumed to deflect to
nonlinear lateral drifts as given in Table 7-7. The
variable d, representing nonlinear deformation
capacities, is expressed in terms of story drift ratio in
percent as defined in Figure 7-1.
For determination of the d values and the acceptable
drift levels using Table 7-7, the ratio of frame to infill
strengths shall be determined considering the expected
lateral strength of each component. If the expected
frame strength is less than 0.3 times the expected infill
strength, the confining effects of the frame shall be
neglected and the masonry component shall be
Seismic Rehabilitation Guidelines
7-19
Chapter 7: Masonry
(Systematic Rehabilitation)
Table 7-6
Linear Static Procedure—m Factors
for Masonry Infill Panels
m Factors
V fre
β = --------V ine
L inf
-------h inf
IO
LS
CP
0.3 ≤ β < 0.7
0.5
1.0
4.0
n.a.
1.0
1.0
3.5
n.a.
2.0
1.0
3.0
n.a.
0.5
1.5
6.0
n.a.
1.0
1.2
5.2
n.a.
2.0
1.0
4.5
n.a.
0.5
1.5
8.0
n.a.
1.0
1.2
7.0
n.a.
2.0
1.0
6.0
n.a.
0.7 ≤ β < 1.3
β ≥ 1.3
Note: Interpolation is permitted between table values.
evaluated as an individual wall component per
Sections 7.4.2 or 7.4.4.
Table 7-7
If the surrounding frame can remain stable following
the loss of an infill panel, infill panels shall not be
subject to limits set by the Collapse Prevention
Performance Level.
If the Nonlinear Dynamic Procedure given in
Section 3.3.4 is used, nonlinear force-deflection
relations for infill panels shall be established based on
the information given in Table 7-7, or on a more
comprehensive evaluation of the hysteretic
characteristics of those components.
Acceptable deformations for existing and new infills
shall be assumed to be the same.
Nonlinear Static Procedure—Simplified Force-Deflection Relations for Masonry Infill Panels
V fre
β = --------V ine
0.3 ≤ β < 0.7
0.7 ≤ β < 1.3
β ≥ 1.3
The Immediate Occupancy Performance Level shall be
met when significant visual cracking of an unreinforced
masonry infill occurs. The Life Safety Performance
Level shall be met when substantial cracking of the
masonry infill occurs, and the potential for the panel, or
some portion of it, to drop out of the frame is high.
Acceptable story drift ratio percentages corresponding
to these general Performance Levels are given in
Table 7-7.
Acceptance Criteria
L inf
--------h inf
c
d
%
e
%
LS
%
CP
%
0.5
n.a.
0.5
n.a.
0.4
n.a.
1.0
n.a.
0.4
n.a.
0.3
n.a.
2.0
n.a.
0.3
n.a.
0.2
n.a.
0.5
n.a.
1.0
n.a.
0.8
n.a.
1.0
n.a.
0.8
n.a.
0.6
n.a.
2.0
n.a.
0.6
n.a.
0.4
n.a.
0.5
n.a.
1.5
n.a.
1.1
n.a.
1.0
n.a.
1.2
n.a.
0.9
n.a.
2.0
n.a.
0.9
n.a.
0.7
n.a.
Note: Interpolation is permitted between table values.
7.5.3
Out-of-Plane Masonry Infills
Unreinforced infill panels with hinf /tinf ratios less than
those given in Table 7-8, and meeting the requirements
for arching action given in the following section, need
not be analyzed for transverse seismic forces.
7-20
7.5.3.1
Stiffness
Out-of-plane infill panels shall be considered as local
elements spanning vertically between floor levels and/
or horizontally across bays of frames.
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
Table 7-8
Maximum hinf /tinf Ratios for which
No Out-of-Plane Analysis is
Necessary
For infill panels not meeting the requirements for
arching action, deflections shall be determined with the
procedures given in Sections 7.4.3 or 7.4.5.
Stiffnesses for existing and new infills shall be assumed
to be the same.
Low
Seismic
Zone
Moderate
Seismic
Zone
High
Seismic
Zone
IO
14
13
8
7.5.3.2
LS
15
14
9
CP
16
15
10
Masonry infill panels shall resist out-of-plane inertial
forces as given in Section 2.11.7. Transversely loaded
infills shall not be analyzed with the Linear or
Nonlinear Static Procedures prescribed in Chapter 3.
The stiffness of infill panels subjected to out-of-plane
forces shall be neglected with analytical models of the
global structural system if in-plane walls or infill panels
exist, or are placed, in the orthogonal direction.
Flexural stiffness for uncracked masonry infills
subjected to transverse forces shall be based on the
minimum net sections of mortared and grouted
masonry. Flexural stiffness for unreinforced, cracked
infills subjected to transverse forces shall be assumed to
be equal to zero unless arching action is considered.
Arching action shall be considered if, and only if, the
following conditions exist.
• The panel is in tight contact with the surrounding
frame components.
The lower bound transverse strength of a URM infill
panel shall exceed normal pressures as prescribed in
Section 2.11.7. Unless arching action is considered, the
lower bound strength of a URM infill panel shall be
limited by the lower bound masonry flexural tension
strength, f t′ , which may be taken as 0.7 times the
expected tensile strength, fte, as determined per
Section 7.3.2.3.
Arching action shall be considered only when the
requirements stated in the previous section are met. In
such case, the lower bound transverse strength of an
infill panel in pounds per square foot, qin, shall be
determined using Equation 7-21.
0.7f m′ λ 2
Q CL = q in = --------------------- × 144
 h inf
 --------
 t inf 
• The product of the elastic modulus, Efe, times the
moment of inertia, If, of the most flexible frame
component exceeds a value of 3.6 x 109 lb-in.2.
• The frame components have sufficient strength to
resist thrusts from arching of an infill panel.
• The hinf /tinf ratio is less than or equal to 25.
For such cases, mid-height deflection normal to the
plane of an infill panel, ∆inf, divided by the infill height,
hinf , shall be determined in accordance with
Equation 7-20.
 h inf
0.002  --------
∆ inf
 t inf 
-------- = ----------------------------------------------------h inf
2
 h inf
-------1 + 1 – 0.002 

 t inf 
FEMA 273
Strength Acceptability Criteria
(7-21)
where
f m′
= Lower bound of masonry compressive
strength equal to fme/1.6, psi
λ2
= Slenderness parameter as defined in Table 7-9
Values of λ2 for Use in
Equation 7-21
Table 7-9
hinf / tinf
5
10
15
25
λ2
0.129
0.060
0.034
0.013
(7-20)
Seismic Rehabilitation Guidelines
7-21
Chapter 7: Masonry
(Systematic Rehabilitation)
7.5.3.3
Deformation Acceptance Criteria
The Immediate Occupancy Performance Level shall be
met when significant visual cracking of a URM infill
occurs. This limit state shall be assumed to occur at an
out-of-plane drift of a story panel equal to
approximately 2%.
The Life Safety Performance Level shall be met when
substantial damage to a URM infill occurs, and the
potential for the panel, or some portion of it, to drop out
of the frame is high. This limit state shall be assumed to
occur at an out-of-plane lateral story drift ratio equal to
approximately 3%.
If the surrounding frame can remain stable following
the loss of an infill panel, infill panels shall not be
subject to limits set by the Collapse Prevention
Performance Level.
Acceptable deformations of existing and new walls
shall be assumed to be the same.
7.6
7.6.1
Anchorage to Masonry Walls
Types of Anchors
Anchors considered in Section 7.6.2 shall include plate
anchors, headed anchor bolts, and bent bar anchor bolts
embedded into clay-unit and concrete masonry.
Anchors in hollow-unit masonry must be embedded in
grout.
Pullout and shear strength of expansion anchors shall be
verified by tests.
7.6.2
Analysis of Anchors
Anchors embedded into existing or new masonry walls
shall be considered as force-controlled components.
Lower bound values for strengths with respect to
pullout, shear, and combinations of pullout and shear,
shall be based on Section 8.3.12 of BSSC (1995) for
embedded anchors.
The minimum effective embedment length for
considerations of pullout strength shall be as defined in
Section 8.3.12 of BSSC (1995). When the embedment
length is less than four bolt diameters or two inches
(50.8 mm), the pullout strength shall be taken as zero.
of anchors with edge distances equal to or less than one
inch (25.4 mm) shall be taken as zero. Linear
interpolation of shear strength for edge distances
between these two bounds is permitted.
7.7
Masonry Foundation Elements
7.7.1
Types of Masonry Foundations
Masonry foundations are common in older buildings
and are still used for some modern construction. Such
foundations may include footings and foundation walls
constructed of stone, clay brick, or concrete block.
Generally, masonry footings are unreinforced;
foundation walls may or may not be reinforced.
Spread footings transmit vertical column and wall loads
to the soil by direct bearing. Lateral forces are
transferred through friction between the soil and the
masonry, as well as by passive pressure of the soil
acting on the vertical face of the footing.
7.7.2
Analysis of Existing Foundations
A lateral-force analysis of a building system shall
include the deformability of the masonry footings, and
the flexibility of the soil under them. The strength and
stiffness of the soil shall be checked per Section 4.4.
Masonry footings shall be modeled as elastic
components with little or no inelastic deformation
capacity, unless verification tests are done to prove
otherwise. For the Linear Static Procedure, masonry
footings shall be considered to be force-controlled
components (m equals 1.0).
Masonry retaining walls shall resist active and passive
soil pressures per Section 4.5. Stiffness, and strength
and acceptability criteria for masonry retaining walls
shall be the same as for other masonry walls subjected
to transverse loadings, as addressed in Sections 7.4.3
and 7.4.5.
7.7.3
Rehabilitation Measures
In addition to those rehabilitation measures provided for
concrete foundation elements in Section 6.13.4,
masonry foundation elements may also be rehabilitated
with the following options:
• Injection grouting of stone foundations
The minimum edge distance for considerations of full
shear strength shall be 12 bar diameters. Shear strength
7-22
• Reinforcing of URM foundations
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
• Prestressing of masonry foundations
• Enlargement of footings by placement of reinforced
shotcrete
• Enlargement of footings with additional reinforced
concrete sections
Procedures for rehabilitation shall follow provisions for
enhancement of masonry walls where applicable per
Section 7.4.1.3.
Hollow masonry unit: A masonry unit whose net
cross-sectional area in every plane parallel to the
bearing surface is less than 75% of the gross crosssectional area in the same plane.
Infill: A panel of masonry placed within a steel or
concrete frame. Panels separated from the surrounding
frame by a gap are termed “isolated infills.” Panels that
are in tight contact with a frame around its full
perimeter are termed “shear infills.”
In-plane wall:
7.8
Definitions
Bearing wall: A wall that supports gravity loads of at
least 200 pounds per linear foot from floors and/or
roofs.
Bed joint: The horizontal layer of mortar on which a
masonry unit is laid.
Cavity wall: A masonry wall with an air space
between wythes. Wythes are usually joined by wire
reinforcement, or steel ties. Also known as a
noncomposite wall.
Clay-unit masonry: Masonry constructed with solid,
cored, or hollow units made of clay. Hollow clay units
may be ungrouted, or grouted.
Clay tile masonry: Masonry constructed with hollow
units made of clay tile. Typically, units are laid with
cells running horizontally, and are thus ungrouted. In
some cases, units are placed with cells running
vertically, and may or may not be grouted.
Collar joint: Vertical longitudinal joint between
wythes of masonry or between masonry wythe and
back-up construction that may be filled with mortar or
grout.
Composite masonry wall: Multiwythe masonry
wall acting with composite action.
Concrete masonry: Masonry constructed with solid
or hollow units made of concrete. Hollow concrete units
may be ungrouted, or grouted.
Head joint: Vertical mortar joint placed between
masonry units in the same wythe.
FEMA 273
See shear wall.
Masonry: The assemblage of masonry units, mortar,
and possibly grout and/or reinforcement. Types of
masonry are classified herein with respect to the type of
the masonry units, such as clay-unit masonry, concrete
masonry, or hollow-clay tile masonry.
Nonbearing wall: A wall that supports gravity loads
less than as defined for a bearing wall.
Noncomposite masonry wall: Multiwythe masonry
wall acting without composite action.
Out-of-plane wall: A wall that resists lateral forces
applied normal to its plane.
Parapet: Portions of a wall extending above the roof
diaphragm. Parapets can be considered as flanges to
roof diaphragms if adequate connections exist or are
provided.
Partially grouted masonry wall: A masonry wall
containing grout in some of the cells.
Perforated wall or infill panel: A wall or panel not
meeting the requirements for a solid wall or infill panel.
Pier: A vertical portion of masonry wall between two
horizontally adjacent openings. Piers resist axial
stresses from gravity forces, and bending moments
from combined gravity and lateral forces.
Reinforced masonry (RM) wall: A masonry wall
that is reinforced in both the vertical and horizontal
directions. The sum of the areas of horizontal and
vertical reinforcement must be at least 0.002 times the
gross cross-sectional area of the wall, and the minimum
area of reinforcement in each direction must be not less
than 0.0007 times the gross cross-sectional area of the
wall. Reinforced walls are assumed to resist loads
Seismic Rehabilitation Guidelines
7-23
Chapter 7: Masonry
(Systematic Rehabilitation)
through resistance of the masonry in compression and
the reinforcing steel in tension or compression.
Reinforced masonry is partially grouted or fully
grouted.
7.9
Ab
Sum of net mortared area of bed joints above
2
and below test unit, in.
Running bond: A pattern of masonry where the head
joints are staggered between adjacent courses by more
than a third of the length of a masonry unit. Also refers
to the placement of masonry units such that head joints
in successive courses are horizontally offset at least
one-quarter the unit length.
A
Shear wall: A wall that resists lateral forces applied
parallel with its plane. Also known as an in-plane wall.
As
Area of equivalent strut for masonry infill, in.
Area of net mortared/grouted section of wall or
2
pier, in.
Area of net mortared/grouted section of
2
masonry infill, in.
Area of reinforcement, in.2
Efe
Expected elastic modulus of frame material, psi
Eme
Elastic modulus of masonry in compression as
determined per Section 7.3.2.2, psi
Expected elastic modulus of reinforcing steel
per Section 7.3.2.6, psi
Shear modulus of masonry as determined per
Section 7.3.2.5, psi
Solid masonry unit: A masonry unit whose net
cross-sectional area in every plane parallel to the
bearing surface is 75% or more of the gross crosssectional area in the same plane.
2
es
An
Ani
Ese
Gme
Solid wall or solid infill panel: A wall or infill panel
with openings not exceeding 5% of the wall surface
area. The maximum length or height of an opening in a
solid wall must not exceed 10% of the wall width or
story height. Openings in a solid wall or infill panel
must be located within the middle 50% of a wall length
and story height, and must not be contiguous with
adjacent openings.
Stack bond: In contrast to running bond, usually a
placement of units such that the head joints in
successive courses are aligned vertically.
Transverse wall: A wall that is oriented transverse to
the in-plane shear walls, and resists lateral forces
applied normal to its plane. Also known as an out-ofplane wall.
Unreinforced masonry (URM) wall: A masonry
wall containing less than the minimum amounts of
reinforcement as defined for masonry (RM) walls. An
unreinforced wall is assumed to resist gravity and
lateral loads solely through resistance of the masonry
materials.
Wythe: A continuous vertical section of a wall, one
masonry unit in thickness.
7-24
4
I
Icol
I
Symbols
f
L
Linf
Moment of inertia of section, in.
Moment of inertia of column section, in.4
Moment of inertia of smallest frame member
4
confining infill panel, in.
Length of wall, in.
Length of infill panel, in.
M
Moment on masonry section, in.-lb
M/V Ratio of expected moment to shear acting on
wall or pier
Lower bound of vertical compressive strength
Pc
for wall or pier, lb
PCE Expected vertical axial compressive force for
load combinations in Equations 3-14 and 3-15,
lb
PCL Lower bound of vertical compressive force for
load combination of Equation 3-3, lb
QCE Expected strength of a component or element at
the deformation level under consideration in a
deformation-controlled action
QCL Lower bound estimate of the strength of a
component or element at the deformation level
under consideration for a force-controlled
action
QE Unreduced earthquake demand forces used in
Equation 3-14
Seismic Rehabilitation Guidelines
FEMA 273
Chapter 7: Masonry
(Systematic Rehabilitation)
QG
V
Vbjs
VCL
Gravity force acting on component as defined in
Section 3.2.8
Shear on masonry section, lb
Expected shear strength of wall or pier based on
bed-joint shear stress, lb
Lower bound shear capacity, lb
Vfre
Lower bound of shear strength based on
diagonal tension for wall or pier, lb
Expected story shear strength of bare frame, lb
Vine
Expected shear strength of infill panel, lb
VmL
Lower bound shear strength provided by
masonry, lb
Expected shear strength of wall or pier based on
rocking, lb
Lower bound shear strength provided by shear
reinforcement, lb
Lower bound of shear strength based on toe
compressive stress for wall or pier, lb
Measured force at first movement of a masonry
unit with in-place shear test, lb
Vdt
Vr
VsL
Vtc
Vtest
a
c
fa
Equivalent width of infill strut, in.
Fraction of strength loss for secondary elements
as defined in Figure 7-1
Wall, pier, or infill inelastic drift percentage as
defined in Figure 7-1
Length of component in direction of shear
force, in.
Wall, pier, or infill inelastic drift percentage as
defined in Figure 7-1
Lower bound of vertical compressive stress, psi
fae
Expected vertical compressive stress, psi
fme
Expected compressive strength of masonry as
determined in Section 7.3.2.1, psi
Expected masonry flexural tensile strength as
determined in Section 7.3.2.3, psi
Expected shear strength of masonry infill, psi
d
dv
e
fte
fvie
fy
f
ye
f ′dt
′
fm
Lower bound of yield strength of reinforcing
steel, psi
Expected yield strength of reinforcing steel as
determined in Section 7.3.2.6, psi
Lower bound of masonry diagonal tension
strength, psi
Lower bound of masonry compressive strength,
psi
FEMA 273
f ′t
Lower bound masonry tensile strength, psi
h
hcol
Height of a column, pilaster, or wall, in.
Height of column between beam centerlines, in.
heff
Height to resultant of lateral force for wall or
pier, in.
Height of infill panel, in.
hinf
k
lbeff
lceff
pD+L
Lateral stiffness of wall or pier, lb/in.
Assumed distance to infill strut reaction point
for beams as shown in Figure C7-5, in.
Assumed distance to infill strut reaction point
for columns as shown in Figure C7-4, in.
Expected gravity stress at test location, psi
rinf
Expected transverse strength of an infill panel,
psf
Diagonal length of infill panel, in.
t
tinf
Least thickness of wall or pier, in.
Thickness of infill panel, in.
vme
Expected masonry shear strength as determined
by Equation 7-1, psi
Average bed-joint shear strength, psi
qine
v
te
vto
Bed-joint shear stress from single test, psi
∆inf
Deflection of infill panel at mid-length when
subjected to transverse loads, in.
α
Factor equal to 0.5 for fixed-free cantilevered
shear wall, or 1.0 for fixed-fixed pier
Ratio of expected frame strength to expected
infill strength
Angle between infill diagonal and horizontal
axis, tan θ = Linf /h inf , radians
β
θ
θb
θc
κ
λ1
Angle between lower edge of compressive strut
and beam as shown in Figure C7-5, radians
Angle between lower edge of compressive strut
and beam as shown in Figure C7-4, radians
A reliability coefficient used to reduce
component strength values for existing
components based on the quality of knowledge
about the components’ properties (see
Section 2.7.2)
Coefficient used to determine equivalent width
of infill strut
Seismic Rehabilitation Guidelines
7-25
Chapter 7: Masonry
(Systematic Rehabilitation)
λ2
Infill slenderness factor
ρg
Ratio of area of total wall or pier reinforcement
to area of gross section
7.10
References
ASTM, latest editions, Standards having the numbers
A615, E22, E518, American Society for Testing
Materials, Philadelphia, Pennsylvania.
BSSC, 1992, NEHRP Handbook for the Seismic
Evaluation of Existing Buildings, developed by the
Building Seismic Safety Council for the Federal
Emergency Management Agency (Report No.
FEMA 178), Washington, D.C.
BSSC, 1995, NEHRP Recommended Provisions for
Seismic Regulations for New Buildings, 1994 Edition,
7-26
Part 1: Provisions and Part 2: Commentary, prepared
by the Building Seismic Safety Council for the Federal
Emergency Management Agency (Report Nos. FEMA
222A and 223A), Washington, D.C.
Masonry Standards Joint Committee (MSJC), 1995a,
Building Code Requirements for Masonry Structures,
ACI 530-95/ASCE 5-95/TMS 402-95, American
Concrete Institute, Detroit, Michigan; American
Society of Civil Engineers, New York, New York; and
The Masonry Society, Boulder, Colorado.
Masonry Standards Joint Committee (MSJC), 1995b,
Specification for Masonry Structures, ACI 530.1-95/
ASCE 6-95/TMS 602-95, American Concrete Institute,
Detroit, Michigan; American Society of Civil
Engineers, New York, New York; and The Masonry
Society, Boulder, Colorado.
Seismic Rehabilitation Guidelines
FEMA 273